Estimating the serial intervals of SARS‐CoV‐2 Omicron BA.4, BA.5, and BA.2.12.1 variants in Hong Kong

Abstract Empirical evidence on the epidemiological characteristics of the emerged SARS‐CoV‐2 variants could shed light on the transmission potential of the virus and strategic outbreak control planning. In this study, by using contact tracing data collected during an Omicron‐predominant epidemic phase in Hong Kong, we estimated the mean serial interval of SARS‐CoV‐2 Omicron BA.4, BA.5, and BA.2.12.1 variants at 2.8 days (95% credible interval [CrI]: 1.5, 6.7), 2.7 days (95% CrI: 2.1, 3.6), and 4.4 days (95% CrI: 2.6, 7.5), respectively, with adjustment for right truncation and sampling bias. The short serial interval for the current circulating variant indicated that outbreak mitigations through contact tracing and case isolation would be quite challenging.


| INTRODUCTION
As one of the genetic variants of concern (VOCs) of SARS-CoV-2 declared by the World Health Organization (WHO), the Omicron (B.1.1.529) variants spread at a rapid rate with novel genetic mutations persistently reported globally. Two emerging Omicron subvariants that were first detected in South Africa in January 2022, that is, BA.4 and BA.5, have risen public health concerns due to their transmission advantages against previous circulating variants. 1,2 Another subvariant of the Omicron lineage, BA.

| Data
We collected line-list contact tracing data of each individual SARS-CoV-2 infection reported from May 1 to July 17, 2022, from the Centre for Health Protection of the Department of Health in Hong Kong.
We extracted the information of symptom onset date, case confirmation date, hospital admission date, contact tracing history, vaccine history, and genotype of the SARS-CoV-2 infected. To obtain SI observations, we constructed the infector-infectee transmission pairs of reported cases based on the contact tracing history.

| Identification of transmission pairs
Based on the contact tracing history for cases with known symptom onset dates provided by the Centre for Health Protection of Hong Kong, we first identified case clusters, comprising a group of epidemiologically linked cases. Case clusters could involve one or multiple generations. Within the case clusters, cases marked by "imported" (cases that acquired infection outside Hong Kong based on the symptom onset dates and recent travel histories) or "local" (cases acquired infection locally and without recent travel history) were considered as the index cases (infector) of the cases in the secondary generation (marked by "close contact with local" or "close contact with imported"). For later generations where cases were all marked by "close contact with local" or "close contact with imported," the infectors were determined only by the reported contact tracing history; that is, cases first exposed to the index cases or previous generations were the infector of the current generation. Infector-infectee transmission pairs were then resolved from case clusters. Infectees with two or more possible infectors were excluded from the analysis. Asymptomatic cases and unlink cases (i.e., cases that were associated with certain contact settings but were not epidemiologically linked with others and cases that were recorded linking to multiple infectors) were excluded from the analysis.
We also excluded the pairs with SIs exceeding 15 days or below À5 days to ensure biologically plausible SI distributions. 5

| Statistical analysis
We denoted S i as the SI for the ith transmission pair, which was defined as the time interval between the illness onset date of the infector and that of his/her associated infectee. We assumed the SI of the BA.4, BA.5, and BA.2.12.1 followed a gamma distribution, denoted by f : ð Þ. For observed negative SI (pre-symptomatic transmission), we added a shift in f : ð Þ. During the early phase of an outbreak, shorter SI is more likely to be identified due to the exponential growth of case numbers. 6 We corrected such sampling bias in f 0 : ð Þ by adjusting the exponential growth with rates r of 0.04, 0.02, and 0.04 per capita per day (estimated from the epidemic curve) for BA.2.12.1, BA.4, and BA.5, respectively. We also conducted sensitivity analysis using different exponential growth rates (from 0.01 to 0.06). The sampling-bias-adjusted distribution function f 0 S i ð Þ is given by 7 : Additionally, we also considered the right truncation of the time interval 8 ; that is, the SI generated by each infector is truncated due to timely case isolation. Thus, the truncation-adjusted distribution function is given by Here, the F 0 : ð Þ is the cumulative density function of f 0 : ð Þ. The T i is the confirmation delay, that is, the time interval between the symptom onset and isolation of the infector for the ith transmission pair. We used the hospital admission date as a surrogate of the isolation date.
For cases without known admission dates, we used the case confirmation date instead. For a total of n transmission pairs identified for a certain type of Omicron subvariant, the likelihood function is given by

| Parameter estimations
The parameters of gamma distribution were estimated by using the

| RESULT AND DISCUSSION
The process of data collection was shown in Figure 1 Figure 3). During an ongoing epidemic, both exponential growth of case numbers and rapid case isolation measures could lead to an underestimation of the SI. 6,8,9 We thus considered such bias in the analysis and the adjusted estimates approaches the intrinsic distribution of SI. 10   addition, selection bias on the transmission pairs could occur during a growth phase of cases as infectors that had more recent symptom onset were more likely to be sampled for an infectee. 6 Nonetheless, we corrected for such bias in our statistical models, and we believe our results were less subjected to this bias. Last, because our sample sizes were small, we could not elucidate the effect of demographic factors (i.e., age and sex), types of contact setting, and vaccinations on the SI distribution of the Omicron subvariants.
In conclusion, our analysis showed a shorter SI for the novel  Research funded by the Tung Foundation is acknowledged for the support throughout the conduct of this study.

CONFLICT OF INTEREST STATEMENT
All authors declared no conflict of interest.

DATA AVAILABILITY STATEMENT
The dataset is not public-available because the data are owned by third parties. Access to these data and permission could be inquired through the Hospital Authority and Department of Health, Hong Kong SAR Government.

PEER REVIEW
The peer review history for this article is available at https://publons. com/publon/10.1111/irv.13105.